An example of calculating the thermal potential for the street network of Nizhny Novgorod
The territory of the city is a complex, heterogeneous system that is in constant change. It is possible to describe the territory and assess the urban environment using spatial objects (factors). The factors describing the territory are different in the nature of influence (positive, negative) and geometric configuration (points, lines, polygons).
It is often difficult to determine the degree of influence of each individual object on the level of development of the territory as a whole or some of its individual aspects. Today, the problem of defining and describing such concepts as "culture", "social sphere", "social tension", "good life", "economic development", "public health" is becoming more and more relevant. The ambiguity of these concepts increases if we want to apply them to different social groups, populations of different ages and genders.
Also, it should be noted that the boundaries of the city in the modern concept are rather arbitrary. Daily migration of the population, transport accessibility of remote areas "blur the border" of the city even more. The concept of agglomeration, which is now widely used, generally reflects the boundaries of the city, but at the same time makes the very concept of the city boundary even more vague.
Despite the problems described above, the analysis and assessment of territories today are one of the promising and interesting areas that allow solving many urgent problems of the urban environment.
The article proposes for consideration a method for analyzing the territory using a "thermal" model. This method is based on the study of potentials created by objects (factors) of various nature (point, linear and areal). Territory analysis using this method makes it possible to move from a set of spatial data (factors) describing the territory to an accurate numerical (point) assessment at each point of the territory.
The potentials studied as part of the analysis of the territory have a physical interpretation - the distribution of heat in media of different dimensions (2D, 3D). This phenomenon can be represented in the form of "thermal" images ("thermal" maps of the territory), giving an idea of the degree of development of the territory, depending on the color intensity of the image.
Territory factors
Territory analysis involves the search and processing of information about the factors influencing the territory and their indicators. Influence factors are objects that affect the surrounding area, possessing a set of characteristics and spatial coordinates. Examples of influence factors are shops, industrial facilities, roads, forests, water bodies.
Influence indicators are objects, reflective the influence of objects and also possessing a set of characteristics and spatial coordinates. Examples of impact indicators: ATMs, billboards, monuments.
In the following presentation, we will use the concept of factors of influence, which combines both terms - factors and indicators of influence.
Below is an example of spatial data that act as influencers.
One of the important stages in the work on the analysis of territories is the stage of collecting and processing initial information. Today, there is a lot of information about the factors of influence on the territory of varying degrees of detail.
Information may be obtained from open sources or restricted access sources. In many cases, open information is sufficient for analysis, although, as a rule, it requires rather laborious processing.
Among open sources, the leader, in our opinion, is the resource - OpenStreetMap (OSM). The information obtained from this source is updated daily around the world.
OpenStreetMap (OSM) resource information is presented in the following formats:
- OSM format. The main format with the ".osm" extension is used to describe XML graphical images - nodes, paths, relationships.
- "Polish format". The text format with the extension ".mp" is used for working with graphics.
- PBF format. Data storage format with the extension ".osm.pbf".
You can also use as sources of information:
— 2 GIS
The resource contains high-quality, monthly processed information, with an excellent 3-level classifier for enterprises and organizations.
— KML (Keyhole Markup Language) files
KML (Keyhole Markup Language) files are a file format used to display geographic data in Google Earth, Google Maps, and Google Maps for mobile applications.
With KML files, you can:
- set various icons and make signatures to indicate places on the surface of the Earth
— create different angles for selected objects by changing the camera position
- use various overlay images
- define styles to customize the display of an object, apply HTML code to create hyperlinks and inline images
- use folders for hierarchical grouping of elements
- dynamically receive and update KML files from remote or local hosts
- get KML data according to changes in the XNUMXD viewer
— Federal Service for State Registration, Cadastre and Cartography "Rosreestr"
The information on the Rosreestr portal is valuable for its content and relevance, but, unfortunately, it does not make it possible to receive graphics for capital construction projects and land plots free of charge. The Rosreestr portal also contains a large amount of restricted access information.
— Statistics bodies
Statistical data is a legitimate source of information about the territory, however, as of today, the data of statistical authorities are available only for a certain number of indicators, mainly in the reports of statistical authorities and reports of regional authorities.
— Information systems of authorities
Qualitative information is contained in the information systems of the authorities, but only a small part of them is published in the public domain and is available for analysis.
Conducting an analysis of the territories does not impose any specific requirements on the composition of information; in fact, you can use everything that you can find, information from open sources is usually interchangeable. However, it should be noted that even the information obtained from the OSM resource alone is enough to make an analysis of unfamiliar territory.
Analysis of the territory using the "thermal" model. Physical interpretation of potentials
As mentioned earlier, the analysis of the territory today is a hot topic and a powerful tool for reasoned attraction of investments in the development of the infrastructure of various urban environments.
The variety of tasks solved by the analysis of territories can be combined into several major areas:
— Obtaining the most interpretable and detailed assessment of the territory at each of its points.
Solving the task, you can get a set of scores at each point of the territory, giving an idea of the level of development of the territory in general, as well as in a certain subject area. Such a subject area can be, for example, culture, industry, trade, etc.
— Determining the most advantageous places for locating investment objects of a certain type (for example, banks, specialized stores, shopping and entertainment centers, etc.) in the selected territory.
— Analysis of the most efficient use of the territory.
This direction allows for a detailed study of the characteristics of the territory, the market situation that has developed in the study area, and the identification of popular options.
— Determining the contribution of one factor to the cost model, using the example of the emergence of new roads and new routes.
– Analysis of different aspects of one territory and analysis of different territories (comparison of territories).
The originality of the method of analysis of the territory proposed in the article using the "thermal" model is the use of indicators of the development of the territory - potentials, presented in numerical terms and reflecting the degree of influence of the object (influence factor) on the territory.
To understand the essence of the study, a few words should be said about the thermal potential itself, and its physical interpretation should be given.
In physics, there are such concepts as force field и force function. The force field has the dimension of energy, the force function has the dimension of force.
For the law of universal gravitation, the force field is defined by the formula:
F=k/r2, where
k is a constant;
r is the distance between interacting objects.
The force function ϕ is given by:
dϕ=-F*dr, where
ϕ is the force field potential;
dϕ, dr are differentials;
r is the distance between interacting objects,
hence ϕ=k/r.
The physical meaning of the potential of the force field ϕ is the work E performed by the force field during the passage of a certain path. In the case of the law of universal gravitation, when the distance to the object changes from r2 to r1, the force function is determined by the formula
E=k*(1/r1-1/r2), where
E is the work done by the force field during the passage of a certain path;
r1, r2 – initial and final position of the object.
For the problem of territory analysis, the influence of objects (factors) on the territory can be considered as a force (power function), and the level of development of the territory, as the total thermal potential (force field) from all objects (factors). In the problems of physics, the thermal potential is temperature, and in the problems of analyzing territories using a “thermal” model, the potential is the total effect of all factors of influence on a point in the territory.
Spatial data are points, lines, polygons. To calculate the potentials, extended spatial data are divided into small fragments. For each fragment, the potential from a point with a multiplier equal to the size of the object fragment (factor) is calculated.
The data are divided into semantic groups according to the principle of close similarity. For example, objects of trade are grouped by goods. There are groups of forest objects, water objects, settlements, transport stops, etc. Groups united in meaning represent a factor. After passing through all objects (factors), we obtain a set of thermal potentials suitable for further processing.
The use of potentials ("thermal maps") allows you to move from spatial data to "thermal" images of objects (factors) of influence on the territory (visualization of potentials). Such a transition makes it possible to determine the degree of presence of the factor at each point of the territory and conduct further analysis, i.e. display different directions of city development in color. Thus, we get a glow of different intensity for each point of the territory.
Examples of "thermal" images of the territory of Nizhny Novgorod in the context of several factors are presented below.
"Heat" map of the city of Nizhny Novgorod, reflecting the factor "Pharmacy chain"
"Heat" map of the city of Nizhny Novgorod, reflecting the factor "Polyclinics for adults"
"Heat" map of the city of Nizhny Novgorod, reflecting the factor "Children's polyclinics"
"Heat" map of the city of Nizhny Novgorod, reflecting the factor "Industrial zones"
"Thermal" images of the territory make it possible to determine the concentration of potentials from various objects of influence. Next, it is necessary to combine the obtained potentials into an integral characteristic, which makes it possible to assess the territory by a large number of factors. This requires a method that allows you to analyze a large amount of information, recognize objects, and reduce the dimension of data, losing the least amount of information. One such method is the Principal Component Analysis (PCA). More details about this method can be found in .
The essence of the method is to find a linear combination of initial parameters that changes most strongly in the area of analysis. For spatial data - the most strongly changing over the territory.
Principal component method identifies objects (factors) that change most across the territory. As a result of the method, new variables appear - the main components, which are more informative than the original data, with the help of which it is easier to analyze, describe and visualize the territory, on which it is easier to build models.
The main components are analytical expressions - the sum of the potentials of the initial factors with some coefficients. However, if any factor has a significant impact on the territory, but does not change across the analyzed territory, the principal component method will not include this factor in the main components.
The principal components are ordered in descending order of information - i.e. distribution over the territory. The first principal components carry much more information than individual factors and describe the territory well. As a rule, when using about a hundred factors, the first principal component carries about 50% of all information (dispersion) on the territory. The principal components do not correlate with each other and can be used for models as characteristics of the territory at each point.
The main component, as some abstractly calculated indicator of the territory, does not have a clear name and classification. However, a combination of factors strongly correlated with the main component allows us to interpret the main components. As a rule, the following factors correlate with the main components:
— the level of infrastructure development;
— transport component of the territory;
— climatic zones;
— the level of development of agriculture;
- the economic potential of the territory.
Further analysis, including clustering, proceeds with the first few significant principal components.
In the figures, one can see a graphical representation of the first principal components on the territory of several cities of the Russian Federation.
The first main component characterizing the level of development of urban infrastructure in the city of Nizhny Novgorod
The first main component characterizing the level of development of urban infrastructure in Yekaterinburg
The first main component characterizing the level of development of urban infrastructure in Kazan
The first main component characterizing the level of development of urban infrastructure in Perm
The first main component characterizing the level of development of urban infrastructure in Samara
The first main component characterizing the level of development of the urban infrastructure of Khabarovsk
Integral characteristics: clustering
The next stage of work on the analysis of territories is the search for zones of the urban environment that are homogeneous in quality. This search is based on the analysis of the values of the principal components at each point of the territory. The task of finding these homogeneous zones can be solved using clustering - the process of grouping territories according to the principle of proximity of a set of characteristics.
Territory clustering has two goals:
- creating a better perceived visualization of the territory;
- allocation of areas for the preparation of individual models.
Territories are clustered according to the selected factors for analysis. These factors can be factors influencing pricing or factors describing some aspect of the development of the territory, for example, the social sphere.
There are two common classical clustering methods: the K-means method and the dendrogram method. When working with territories, the K-means method has proven itself well, a feature of which is the “growing” of a cluster by attaching new objects to growth points. The advantages of the K-means method lies in the similarity of its work to the natural process of territory formation: the integration of similar, rather than the separation of dissimilar.
Using the K-means method, a calculation was made for Nizhny Novgorod (Figure below).
Compliance of clusters with the level of development of the territory on the example of the city of Nizhny Novgorod
With the proposed approach, you can get an idea of the territory on various topics. Topics of interest to us may be, for example, the level of development of urban infrastructure, the level of “eliteness” of the territory, the level of development of culture, the social component of the development of the territory. These themes are poorly defined integral concepts, and consist of many interrelated factors.
With some algorithm for selecting parameters for analysis (including with the involvement of experts), we will get thematic maps that give an idea of one aspect of the development of the territory.
The integral characteristics are understood as the first principal components, primarily the most informative first principal component, and the clustering of the territory according to the selected parameters.
Thematic maps of the first principal components for various aspects of development are presented in the figures below.
Thematic map "Objects of culture" on the example of the city of Nizhny Novgorod
Thematic map "Social sphere" on the example of the city of Nizhny Novgorod
Integral characteristics make it possible to understand the characteristics of the territory, operating with a variety of factors with minimal loss of information.
In conclusion, it is worth noting once again that today the analysis of territories is an extremely important step in solving the problems of developing the urban environment, choosing places for investing in construction, finding the most advantageous location for new facilities, and other tasks.
The method of territory analysis proposed in the article using the “thermal” model from factors of different nature is not critical to the set of factors, i.e. does not impose restrictions and requirements on the initial information.
The diversity and redundancy of the source information, as well as the ability to use open data provides unlimited perspectives for the analysis of any territories of the world.
In the next publications devoted to the problems of territory analysis, we plan to reveal the features of building models using principal components and methods for their implementation for such tasks as:
– choosing the best place when placing a new object;
— construction of a price surface for a certain category of objects using market value;
-assessment of the profitability of a certain type of activity depending on the location of the objects.
It is also planned to present methods for the reverse transition from the main components to the factors, which in turn allows you to get a model from the factors for a given territory.
Source: habr.com